PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Searching for Diophantine quintuples

Volume 173 / 2016

Mihai Cipu, Tim Trudgian Acta Arithmetica 173 (2016), 365-382 MSC: Primary 11D09; Secondary 11B37, 11J86, 11D45. DOI: 10.4064/aa8254-2-2016 Published online: 18 May 2016


We consider Diophantine quintuples $\{a, b, c, d, e\}$. These are sets of positive integers, the product of any two elements of which is one less than a perfect square. It is conjectured that there are no Diophantine quintuples; we improve on current estimates to show that there are at most $5.441\cdot 10^{26}$ Diophantine quintuples.


  • Mihai CipuSimion Stoilow Institute of Mathematics
    of the Romanian Academy
    Research unit no. 5, P.O. Box 1-764
    RO-014700 Bucureşti, Romania
  • Tim TrudgianMathematical Sciences Institute
    The Australian National University
    Canberra, Australia

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image